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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 11: 1. x ∈( 0;$\pi$ ) sao cho cos$^{2}$2x – cos2x=0

Home/ Toán Lớp 11: 1. x ∈( 0;$\pi$ ) sao cho cos$^{2}$2x – cos2x=0

Toán Lớp 11: 1. x ∈( 0;$\pi$ ) sao cho cos$^{2}$2x – cos2x=0

Tháng Hai 5, 2023 Toán học 2 Comments 0 views

Toán Lớp 11: 1. x ∈( 0;$\pi$ ) sao cho cos$^{2}$2x – cos2x=0

Comments ( 2 )

  1. trucoanh55
    trucoanh55
    5 Tháng Hai, 2023 at 8:42 chiều
    Reply

    Gửi bạn
    toan-lop-11-1-0-pi-sao-cho-cos-2-2-cos2-0

  2. khanhngantoan
    khanhngantoan
    5 Tháng Hai, 2023 at 8:42 chiều
    Reply
    ~rai~
    \(\cos^22x-\cos2x=0\\\Leftrightarrow \cos2x(\cos2x-1)=0\\\Leftrightarrow \left[\begin{array}{I}\cos2x=0\\\cos2x-1=0\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}2x=\dfrac{\pi}{2}+k\pi\\\cos2x=1\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x=\dfrac{\pi}{4}+k\dfrac{\pi}{2}\\2x=k2\pi\end{array}\right.\\\Leftrightarrow \left[\begin{array}{I}x_1=\dfrac{\pi}{4}+k\dfrac{\pi}{2}\\x_2=k\pi.\end{array}\right.\quad(k\in\mathbb{Z})\\\text{Do x}\in(0;\pi)\\TH1:0<x_1<\pi\\\Leftrightarrow 0<\dfrac{\pi}{4}+k\dfrac{\pi}{2}<\pi\\\Leftrightarrow -\dfrac{\pi}{4}<k\dfrac{\pi}{2}<\dfrac{3\pi}{4}\\\Leftrightarrow -\dfrac{1}{2}<k<\dfrac{3}{2}\\\text{Do k}\in\mathbb{Z}\Rightarrow k\in\{0;1\}\\\Rightarrow x=\dfrac{\pi}{4};x=\dfrac{3\pi}{4}.\\TH2:0<x_2<\pi\\\Leftrightarrow 0<k\pi<\pi\\\Leftrightarrow 0<k<1\\\text{Do k}\in\mathbb{Z}\Rightarrow \text{Không có số nguyên k thỏa mãn.}\\\Rightarrow x=\varnothing.\\\text{Vậy phương trình có 2 nghiệm thuộc (0;}\pi)\quad\text{là}\quad x=\dfrac{\pi}{4};x=\dfrac{3\pi}{4}.\)
     

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222-9+11+12:2*14+14 = ? ( )

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